the protestor was not saying that she'd read that none of warren's children had ever attended a single day of public school. and there is no reasonable reading of the assertion by warren to mean that she was stating that her children attended a mixture of public and private schools.
The exchange was literally two seconds long, not nearly long enough for you to know the intent of either woman, it's likely neither of them knew. You're interpreting it that way because you choose to, not because your observation is fact.
Elizabeth Warren has two children, they both attended public school, one for the entirety of her schooling, the other for 5 years. These are indisputable facts. An indisputable fact can never be a lie.
We really aren't ready for a woman president.